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The aim of this study was to model, based on the overall distribution of extreme values, the probability of occurrence of a particular level of annual maximum daily rainfall in three Brazilian regions (Midwest, Southeast and South) and study their behavior over the past 71 years. The parameters of the general distribution of extreme values were estimated by the maximum likelihood method. The Mann–Kendall test showed that there is a positive trend in the annual maximum daily rainfall data series. The non-stationarity was rejected by the augmented Dickey–Fuller test supporting the use of the density function of extreme value distribution to describe the values of the occurrence of annual maximum daily rainfall. The Kolmogorov–Smirnov/Lilliefors goodness-of-fit test showed the good fit of the studied variable to the probability distribution function. The Midwest region has a return period of more frequent annual maximum daily rainfall below 300 mm in comparison with other regions. There is a clear change in the behavior of this extreme event in the Southern region. According to the literature, in past decades annual maximum daily rainfall of 248 mm has been estimated for a return period of 100 years for the state of Santa Catarina-South region, while the results found with the current series, annual maximum daily rainfall of 250 mm was estimated for a return period of 10 years. Extreme annual maximum daily rainfalls for return periods smaller were also found in other regions.

The aim of this study was to model the occurrence of extreme dry spells in the Midwest, Southeast and Southern regions of Brazil and estimate the return period of the phenomenon indicating the time when the occurrence is more severe. The generalized extreme value distribution was the best fit for a series of maximum dry spell number and the parameters estimated by the maximum likelihood method. The data series adherence to the probability distribution was verified by the Kolmogorov–Smirnov test and the percentile–percentile charts. The positive trend of dry spells was verified by the Mann–Kendall test and non-stationarity rejected by Dickey–Fuller and augmented Dickey–Fuller tests. The irregular distribution of rainfall in the growing season for the Midwest region has increased the number of dry spells. The increase of rainy days in the Southeast and the South resulted in a decrease of dry spells in these regions. Regarding the return period of one year, dry spells occurred from 5 to 25 days in the Midwest region meaning a loss of productivity for Brazilian agriculture if it happened between the flowering and grain filling phases, making it, therefore the region with the largest agricultural risk. When the intensity of the dry spells was analyzed for different return periods, the Southern region was the most vulnerable.

The purpose of this study is to evaluate the accuracy of the estimation the monthly mean temperature simulated by the PRECIS model—scenarios A2 and B2 of the IPCC—for Brazilian regions and to develop a Kalman filter to correct the systematic errors of the model for the months of January to June 2010. With a regionalized model, PRECIS aims to reproduce the main features of the climate in complex terrains. The temperature estimates for January to June 2010 are based on linear regression of PRECIS simulations in each pixel of the domain for two time periods, 1961–1990 and 2070–2100. These initial estimates are adapted to 1142 observing stations by a correction using the vertical temperature gradient of the Standard Atmosphere and the difference between model and real topography. The analysis was performed using monthly observed mean temperature data from meteorological stations, along with 1142 simulated data. The PRECIS model with systematic errors was ameliorated by the application of the filter resulting in an improved mean temperature prediction of 66% above the mean square error for the dry months and above 49% for the wet months, for both scenarios under study. At the half-way point, the improvement was 68% for the A2 scenario and 69% for scenario B2.